In the next coming years, the International Space Station (ISS) plans to launch several small-sat missions powered by lithium-ion battery packs. An extended version of such mission requires dependable, energy dense, and durable power sources as well as system health monitoring. Hence a good health estimation framework to increase mission success is absolutely necessary as the devices are subjected to high demand operating conditions. This paper describes a hierarchical architecture which combines data-driven anomaly detection methods with a fine-grained model-based diagnosis and prognostics architecture. At the core of the architecture is a distributed stack of deep neural network that detects and classifies the data traces from nearby satellites based on prior observations. Any identified anomaly is transmitted to the ground, which then uses model-based diagnosis and prognosis framework to make health state estimation. In parallel, periodically the data traces from the satellites are transported to the ground and analyzed using model-based techniques. This data is then used to train the neural networks, which are run from ground systems and periodically updated. The collaborative architecture enables quick data-driven inference on the satellite and more intensive analysis on the ground where often time and power consumption are not constrained. The current work demonstrates implementation of this architecture through an initial battery data set. In the future we propose to apply this framework to other electric and electronic components on-board the small satellites.